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UNIT I
Basic Principles of Machine Design
Consists of
1. Introduction
2. Constructional Elements of Transformer
3. Constructional Elements of Rotating Machines
4. Classification of design problems
5. Magnetic loading
6. Electrical loading
7. Output Equation
8. Standard Specifications
1.Introduction
The problem of design and manufacture of electrical machinery is
to build as
economically as possible, a machine which fulfils a certain set
of
specifications and guarantees.
The major considerations to evolve good design are
1. Cost
2. Durability
3. Compliance with performance criteria as laid down in
specifications
2. Constructional Elements of Transformer
1.Iron Core
2.Primary and Secondary Winding
3.Transformer Tank
4.Cooling Tubes
3. Constructional elements of rotating machines
1.Stator
2.Rotor
3.Others
3.(a)DC Machine
1. Stator:
Yoke,Field Pole, Pole Shoe, Field Winding, Interpole
2. Rotor:
Armature Core, Armature Winding , Commutator
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3. Others:
Brush and Brush holder
3.(b)Squirrel cage induction motor
1. Stator:
Frame, stator core and stator winding
2. Rotor:
Rotor core, rotor bars and Endrings
4. Classification of design problems
1. Electromagnetic Design
2. Mechanical Design
3. Thermal Design
4. Dielectric Design
5. Magnetic loading
1. Total Magnetic Loading (TML)
TML=Total flux entering and leaving the armature
TML=p
2. Specific Magnetic Loading (SML)
SML=(Flux per pole)/Area Under a pole SML=(p)/(DL)
6. Electric Loading
1. Total Electric Loading (TEL)
TEL=sum of currents in all the conductors on the armature
TEL=IzZ
2. Specific Electric Loading (SEL)
SEL=(Total Armature ampere conductors)
Armatue periphery at airgap
SEL=(IzZ)/D
7. Output Equation
The output of a machine can be expressed in terms of its
main
dimensions, specific magnetic and electric loadings and
speed.
Pa=CoD2Ln
Where Output coefficient Co=2Bavac*10-3
8. Standard Specifications
The standard specifications of electrical machines are
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1. Standard ratings of machines
2. Types of enclosure
3. Standard dimensions of conductors to be used
4. Method of marking ratings and name plate details
5. Performance specifications to be met
6. Types of insulation and permissible temperature loss
7. Permissible loss and range of efficiency
8. Procedure for testing of machine parts and machines
9. Auxiliary equipments
Name Plate Details
KW or KVA rating of machine
Rated working voltage
Operating speed
Full load current
Class of insulation
Frame size
Manufacturers name
Serial number of the machine
ISO numbers with year
IS 325-1966 : Specifications for 3ph induction motor
IS 4029-1967 : Guide for testing 3ph induction motor
IS12615-1986 : Specifications for energy efficient induction
motor
IS13555-1993 : Guide for selection & application of 3ph
induction motor for
different types of driven equipment
IS8789-1996 : Values of performance characteristics for 3ph
induction motor
IS 12066-1986 : 3ph induction motors for machine tools
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UNIT II
DC Machines
Consists of
- Constructional Elements
- Output Equation
- Choice of specific loadings
- Selection of number of poles
- Length of airgap
- Armature design
- Field system design
- Commutator and brushes
- Efficiency and Losses
1. Constructional Elements
(i) Armature
(1) winding
(2) core
(3) commutator
(ii) Field
(1) winding
(2) core
(3) pole shoe
(iii) Frame
2. Output equation
The output of a machine can be expressed in terms of its main
dimensions,
specific magnetic and electric loadings and speed.
Pa=CoD2Ln
Where Output coefficient Co=2Bavac*10
-3
3. Choice of specific loading
3.1 Choice of specific magnetic loading
Depends on, 1. Flux density in teeth
2. Frequency of flux reversal
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3. Size of machine
(i) Flux density
Large values of Bav in teeth increases field mmf.
Higher mmf results in increase of iron loss, cu loss & cost
of cu.
Bav does not exceed 2.2wb/m2
(ii) Frequency of flux reversal
If f is high then iron losses in arm. Core & teeth would be
high.
So high value of Bav is not used.
(iii) Size of machine
If size increases Bav also increases.
As the dia increases the width of the tooth also increases,
permitting increased
value of Bg without saturation.
Bg bet 0.55 to 1.15Wb/m2 & Bav 0.4 to0.8 wb/m2
3.2 Choice of specific electric loading
Depends on, 1. Temperature rise
2. Speed of machine
3. Voltage
4. Size of machine
5. Armature reaction
6. Commutation
(i) Temperature rise
Higher ac results in high temp rise of wdgs.
Temp rise depends on type of enclosure & cooling techniques
employed.
Ex. In m/cs. Using class F insulation which can withstand a
temp. of 155c,
the value of ac can be approx. 40% higher than that used in
m/cs. Designed for class
A insulation which can withstand a temp. of only 105c.
(ii) Speed of machine
If N is high, ventilation of the machine is better &
therefore greater losses can
be dissipated. Thus higher ac can be used for high N.
(iii) Voltage
In high V m/cs large space is reqd. for insulation &
therefore less space for
conductors.
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Ie. Space left for conductors is less & therefore we should
use a small value of
ac.
(iv) Size of m/c
In large size m/cs it is easier to find space for accommodating
conductors.
Hence ac can be increased with increase in dimensions.
(v) Armature reaction
With high ac, arm. Reaction will be severe. To counter this the
field mmf is
increased & so cost goes high.
(vi) Commutation
Ac=Iz*Z
D*
High value of ac will have either (i) Large Z OR
(ii) small dia D
(i) M/c have large Z having large no. of turns; L is
proportional to square
of no. of turns; so large ac
(ii) If small dia, it is not possible to use wide slots because
otherwise the
space left for teeth will become smaller giving rise to high B
in them.
Only way is us ting deeper slots to use. But the deeper slots
increases
the L value.
Increased L increases reactance voltage which delays the
commutation.
High ac worsens the commutation condition in m/cs.
From commutation point of view small ac is desirable.
Ac lies bet. 15,000 to 50,000amp.cond/m
4. Selection of no. of poles
The aim of the designer to select the main dimensions as will
result in the
minimum cost and yet at the same time meet the desired
specifications.
As for as the magnetic circuit is concerned it is necessary to
choose a suitable
no. of poles and to suitably proportion them. A proper design of
the electric circuit
requires suitable dimensions which result in satisfactory
arrangements for wdg and
commutator.
For choice of no. of poles let us assume D,L,Bav & ac are
const.P only
variable.
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(i) Frequency
F=pn/2
If p is high then f also increases which may lead to excessive
iron
losses in
arm. Teeth and core.
In case of high speed turbo alternators the no. of poles used is
2
oterwise the frequency will become high giving rise to excessive
iron losses.
(ii) Weight of iron parts
No. of poles effects the no. of parts in magnetic circuit
(a) Yoke area
For 2 pole m/c
Total flux around the airgap is const.=T
Flux per pole = T/2
At yoke the flux further divided into 2 parts &
therefore
Yoke has to carry a flux of T/4
For 4 pole m/c
Flux per pole = T/4
At yoke the flux further divided into 2 parts &
therefore
Yoke has to carry a flux of T/8
Thus if the no. of poles is doubled, the flux carried by yoke is
halved.
The flux carried by yoke is inversely proportional to no. of
poles.
Therefore by using no. of poles, the area of cross section of
yoke is
proportionately decreased.
(b) Armature core area
The flux per pole divides itself in 2 paths in the armature
core.
For 2 pole m/c
Flux in the arm. = T/4
For 4 pole m/c
Flux in the arm. = T/8
Thus we can safely use a large no. of poles so as to reduce the
wt of
iron in the yoke.But increase in no. of poles would result in
higher iron
loss in arm. Core owing to increased frequency of flux
reversals.
We can examine this here.
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For 2 pole m/c
Eddy ct loss in arm. Core Bc2f2 Bc2(pn/2)2
s (T/4A2)2*(2*n/2)2
(T2n2)/16A22
For 4 pole m/c
Eddy ct loss in arm. Core Bc2f2 Bc2(pn/2)2
s (T/8A4)2*(4*n/2)2
(T2n2)/1642
5. Length of airgap
A small gap is provided between the rotor and stator to avoid
the
friction
between the stationary and rotating parts.
A large value of airgap results in
1. Lesser noise
2. better cooling
3. Reduced pole face losses
4. Reduced circulating losses
5. Less distortion of field form
6. Higher field mmf which reduces armature reaction
Length of airgap (lg) = (0.5 to 0.7)*ac*
1,600,000*Bg*Kg
6. Armature Design
The armature of a dc machine consists of core and winding.
The armature core is cylindrical in shape with slots on the
outer periphery of
the armature. The core is formed with circular laminations of
thickness 0.5mm. The
winding is placed on the slots in the armature core. The design
of armature
core involves the design of main dimensions D & L, number of
slots, slot dimensions
and depth of core.
(i) Number of armature slots
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The factors to be considered for selection of number of armature
slots
are
(i) slot width
(ii) cooling of armature conductors
(iii) flux pulsations
(iv) commutation
(v) cost
(ii) Slot dimensions
The dimensions of the slot are slot width and depth. Usually the
slot
area is estimated from the knowledge of conductor area and slot
space
factor. The slot factor lies in the range of 0.25 to 0.4 &
the value
depends on the thickness of insulation.
Slot area = (Conductor Area)/(Slot space factor)
The following factors can be considered before finalising the
slot
dimensions.
1. Flux density in tooth
2. Flux pulsations
3. Eddy current loss in conductors
4. Reactance voltage
5. Fabrication difficulties
(iii) Depth of armature core
The depth of armature cannot be independently designed, because
it
depends on the
(1) diameter of armature
(2) inner diameter of armature
(3) depth of slot
Depth of core = (1/2)*( /Li*Bc)
Where
= flux per pole
Li= Net iron length of the armature
Bc= flux density in the core
7. Field system design
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The field system consist of
(i) poles
(ii) poloe shoes
(iii) field winding
The two types of the field winding are
(i) shunt field winding
(ii) series field winding
The shunt field winding consists of large number of turns made
of thin
conductors, because the current carried by them is very low. The
series
field winding is designed to carry heavy current and so it is
made of
thick conductors.
7.1 Design of shunt field winding
The design of shunt field winding involves the determination of
the
following
(i) Dimensions of the main field pole
(ii) Dimensions of the field coil
(iii) Dimensions of the field conductor
(iv) Current in the shunt field winding
(v) Resistance of the field coil
(vi) Number of turns in the field coil
(vii) Losses in the field coil
(i) Dimensions of the main field pole
The dimensions of the rectangular field pole are
(1) Area of cross-section
(2) Length
(3) Width
(4) Height of pole body
For cylindrical poles the dimensions has to be estimated instead
of
length and width.
(ii) Dimensions of field coil
The field coils are former wound & placed on the poles. The
field coils
may have rectangular or circular cross-section, depending on the
type
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of poles. The dimensions of the field coil are depth, height
& length of
mean turn of field coil.
(iii) Current in the shunt field winding
The shunt field current can be estimated from the knowledge
of
voltage across field coil and the resistance of field coil. Each
pole of a
dc machine carries one field coil and all the field coils are
connected in
series to form shunt field winding. Hence the voltage across
each field
coil is given by
voltage across each field coil, Ef =voltage across shunt field
winding
Number of poles
field current= Ef/Rf
(iv) Resistance of field coil
The resistance of the field coil can be estimated from the
knowledge of
resistivity of copper, length of mean turn of field coil and
area of cross
section of field conductor.
(v) Dimensions of field conductor
The dimensions of the are area of cross section and diameter.
The area
of cross section of the field conductor can be estimated from
the
knowledge of field current (If) & current density (f). The
usual range
of current density in the field conductor is 1.2 to 3.5
A/mm2.
(vi) Number of turns in field coil
When the ampere turns to be developed by the field coil is known
the
turns can be estimated from the knowledge of field current.
(vii) Power loss in the field coil
The power loss in the field coil is copper loss which depends
on
resistance and current. Heat developed in the field coil due to
this loss
and heat is dissipated through the surface of the coil. If there
is no
sufficient surface for heat dissipation then heat accumulates,
which
may lead to damage(or burning) of the coil.
In field coil design the loss dissipated per unit surface area
is specified
and from which the required surface area can be estimated. The
surface
area of field coil depends on length of mean turn, depth and
height of
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field coil. Usually the length of mean turn is estimated in
order to
provide the required surface area.
The heat can be dissipated from all the 4 sides of a coil ie.,
inner, outer,
top & bottom surface of the coil.
8. Design of commutator and brushes
The commutator and brush arrangement are used to convert the
bidirectional internal current to unidirectional external
current or
viceversa. The current flows through the brushes mounted on
the
commutator surface. The brushes are located at the magnetic
neutral
axis which is midway between adjacent poles.
When a armature conductor pass through the magnetic neutral
axis, the
current in the conductor reverses from one direction to the
other. Since
the brushes are mounted on magnetic neutral axis, the coil
undergoing
current reversal is short circuited by carbon brush. During this
short
circuit period, the current must be reduced from its original
value to
zero and then built up to an equal value in the opposite
direction. This
process is called the time of commutation.
The process of commutation is classified into
(i) Resistance commutation
(ii) Retarted commutation
(iii) Accelerated commutation
(iv) Sinusoidal commutation
9. Efficiency and losses
Efficiency of a machine is defined as the ratio of output of the
machine
to the input supplied to the machine.
Losses in the dc machine are given as follows
(i) Iron loss
(ii) Copper loss
(iii) Windage and friction loss
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UNIT III
Transformers
This unit consists of
- Introduction
- Types
- Output equation
- Design of cores
- Overall dimensions
- Design of winding
- Design of tank with cooling tubes
- Efficiency and losses
1. Introduction
The transformer is based on two principles: first, that an
electric
current can produce a magnetic field (electromagnetism), and,
second that a
changing magnetic field within a coil of wire induces a voltage
across the ends
of the coil (electromagnetic induction). Changing the current in
the primary
coil changes the magnetic flux that is developed. The changing
magnetic flux
induces a voltage in the secondary coil.
An ideal transformer is shown in the adjacent figure. Current
passing through
the primary coil creates a magnetic field. The primary and
secondary coils are
wrapped around a core of very high magnetic permeability, such
as iron, so
that most of the magnetic flux passes through both the primary
and secondary
coils.
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Induction law
The voltage induced across the secondary coil may be calculated
from Faraday's law
of induction, which states that:
where Vs is the instantaneous voltage, Ns is the number of turns
in the secondary coil
and is the magnetic flux through one turn of the coil. If the
turns of the coil are
oriented perpendicular to the magnetic field lines, the flux is
the product of the
magnetic flux density B and the area A through which it cuts.
The area is constant,
being equal to the cross-sectional area of the transformer core,
whereas the magnetic
field varies with time according to the excitation of the
primary. Since the same
magnetic flux passes through both the primary and secondary
coils in an ideal
transformer, the instantaneous voltage across the primary
winding equals
Taking the ratio of the two equations for Vs and Vp gives the
basic equation for
stepping up or stepping down the voltage
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2. Types
(i) Core
(ii) Shell
(i) Core
The iron core is made of thin laminated silicon steel (2-3 %
silicon)
Pre-cut insulated sheets are cut or pressed in form and placed
on the top of
each other .The sheets are overlap each others to avoid (reduce)
air gaps.
1. Easy in design
2. Has low mechanical strength due to non bracing of
windings
3. reduction of leakage reactance is not easily dismantled.
4. The assembly can be easily dismantled for repair work.
5. Better heat dissipation from windings.
6. Has longer mean length of core and shorter mean length of
coil
turn. Hence best suited for Extra High voltage(EHV)
requirements.
(ii) Shell
1. Comparatively complex
2. High mechanical strength
3. Reduction of leakage reactance is highly possible
4. It cannot be easily dismantled for repair work.
5. Heat is not easily dissipated from windings since it is
surrounded
by core
6. It is not suitable for EHV requirements.
3. Output Equation
The equation which relates the rated KVA output of a transformer
to
the area of core & window is called output equation.
In transformers the output KVA depends on flux density and
ampere turns.
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The flux density is related to core area & the ampere turns
is related to
window area.
The low voltage winding is placed nearer to the core in order to
reduce
the insulation requirement. The space inside the core is called
window & it is
the space available for accommodating the primary and secondary
winding.
The window area is shared between the winding and their
insulations.
Induced emf in a transformer E=4.44fmT volts
Window space factor Kw = Ac/Aw
Where Ac = Conductor area in window
Aw = Total area of window
Current density = Ip/ap=Is/as;
Where ap = area of cross-section of primary conductor
as = area of cross-section of secondary conductor
Ampere turns AT = IpTp=IsTs
Where Tp,Ts = Number of turns in primary & secondary
Total copper Area in window,Ac= 2AT/;
KVA rating Q = Vp*Ip*10-3
Q = 2.22*f*Bm*Ai*Aw*Kw* *10-3
3.1Output equation of 3 phase Transformer
Induced emf in a transformer E=4.44fmT volts
Window space factor Kw = Ac/Aw
Where Ac = Conductor area in window
Aw = Total area of window
Current density = Ip/ap=Is/as;
Where ap = area of cross-section of primary conductor
as = area of cross-section of secondary conductor
Ampere turns AT = IpTp=IsTs
Where Tp,Ts = Number of turns in primary & secondary
Total copper Area in window,Ac= 4AT/;
KVA rating Q = 3*Vp*Ip*10-3
Q = 3.33*f*Bm*Ai*Aw*Kw* *10-3
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4. Design of cores
For core type transformer the cross-section may be
(i) Rectangular
(ii) Square
(iii) Stepped
When circular coils are required for distribution and power
transformers, the
square and stepped cores are used.
For shell type transformer the cross-section may be
Rectangular
When rectangular cores are used the coils are also rectangular
in shape.
The rectangular core is suitable for small and low voltage
transformers.
In square cores the diameter of the circumscribing circle is
larger than
the diameter of stepped cores of same area of cross-section.
Thus when
stepped cores are used the length of mean turn of winding is
reduced with
cosequent reduction in both cost of copper & copper loss.
However with a
large number of steps a large number of different sizes of
laminations have to
be used. This results in higher labour charges for shearing and
assembling
different types of laminations.
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Ratio
Square core
Cruciform
core
3-stepped
core
4stepped
core
Agi/Area of circumscribing circle
0.64
0.79
0.84
0.87
Ai/Area of circumscribing circle
0.58
0.71
0.75
0.78
Core area factor, Kc = Ai/d2
0.45
0.56
0.6
0.62
Where Agi = Gross core area
Ai = Net core area
5. Overall Dimensions
The main dimensions of the transformer are
(i) Height of window(Hw)
(ii) Width of the window(Ww)
The other important dimensions of the transformer are
(i) width of largest stamping(a)
(ii) diameter of circumscribing circle
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(iii) distance between core centres(D)
(iv) height of yoke(Hy)
(v) depth of yoke(Dy)
(vi) overall height of transformer frame(H)
(vii) overall width of transformer frame(W)
6. Design of winding
The transformer has one low voltage winding and one high
voltage
Winding. The design of winding involves the determination of
number of
Turns & area of cross-section of the conductor used for
winding. The number
Of turns is estimated using voltage rating & emf per turns.
The area of cross-
section is estimated using rated current & current
density.
Usually the number of turns of low voltage winding is estimated
first
using the given data & it is corrected to nearest integer.
Then the number of
turns of high voltage winding are chosen to satisfy the voltage
rating of the
transformer.
Number of turns in low voltage winding , T1=V1/Et=AT/I1
Number of turns in high voltage winding , T2=T1*V2/V1
V1,V2 = Voltage in low & high values
Rated current in a winding = (KVA per phase*10-3
)/Voltage rating of the winding
7.Design of Tank with cooling Tubes
The transformers are provided with cooling tubes to increase the
heat
dissipating area. The tubes are mounted on the vertical sides of
the transformer tank.
But the increase in dissipation of heat is not proportional
increase in area, because the
tubes would screen some of the tank surface preventing
radiations from the screened
surface. On the other hand the tubes will improve the
circulation of oil. This improves
the dissipation of loss by convection. The circulation of oil is
due to more effective
pressure heads produced by columns of oil in tubes.
The improvement in loss dissipation by convection is equivalent
to loss
dissipated by 35% of tube surface area. Hence to account for
this improvement in
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dissipation of loss by convection an additional 35% tube area is
added to actual tube
surface area or specific heat dissipation due to convection is
taken as 35% more than
that without tubes.
Dissipating surface of tank = St
Dissipating surface of tubes = XSt
Total area of walls & tubes = St(1+X)
Loss dissipated per area of = Total loss dissipated/Total
area
Surface
= (12.5+8.8X)/(1+X)
Total loss = Pi+Pc
Total Area of cooling tubes = (1/8.8)*[(Pi+Pc/)-12.5St]
Total number of tubes = Total Area of tubes/Area of each
tube
8. Efficiency and losses
In an ideal transformer, the power in the secondary windings is
exactly
equal to the power in the primary windings. This is true for
transformers with a
coefficient of coupling of 1.0 (complete coupling) and no
internal losses. In real
transformers, however, losses lead to secondary power being less
than the primary
power. The degree to which a real transformer approaches the
ideal
conditions is called the efficiency of the transformer:
Efficiency = Pout/Pin*100%
where Pout and Pin are the real output and the input powers.
Apparent and reactive
powers are not used in efficiency calculations.
Losses in a transformer are
(i) Core losses
(ii) Copper losses
There are no rotating parts in the transformer so there are no
rotational
losses.
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UNIT IV
INDUCTION MOTOR
Consists of
- Construction
- Output equation
- Choice of loadings
- Main dimensions
- Stator winding
- Stator core
- Length of airgap
- Choice of rotor slots
- Design of Squirrel cage rotor
- Design of Wound rotor
1. Construction
Consists of two major parts
(i) Stator
(ii) Rotor
Stator consists of
(i) Core
(ii) Winding
Rotor is of two types
(i) Squirrel cage
(ii) Wound rotor
Squirrel cage rotor consists of
(i) core
(ii) copper or aluminium bars
(iii) end rings
Wound rotor consists of
(i) core
(ii) winding
(iii) slip rings & brushes
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2. Output Equation
Output equation of ac machine is relation of KVA rating of
the
machine to the specific loadings and main dimensions.
KVA = Co*D2*L*ns
Output coefficient = 11Kws*Bav*ac*10-3
The rating of an induction motor is sometimes given in horse
power(HP) . This rating refers to the power output at the shaft
of the
motor. The KVA input for the motor can be calculated from
the
following formula.
KVA = (HP*0.746)/(*cos)
Cos = Power Factor
= Efficiency
Squirrel cage Induction motor
varies from 72% to 91%
Power factor varies from 0.66 to 0.9
Slip Ring Induction motor
varies from 84% to 91%
Power factor varies from 0.7 to 0.92
3. Choice of specific loadings
The value of output coefficient depends upon the choice of
specific electric
loading(ac) & specific magnetic loading(Bav).
Choice of specific electric loading depends on
1. copper loss
2. Temperature rise
3. voltage rating
4. overload capacity
Choice of specific magnetic loading depends on
1. Power factor
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2. iron loss
3. overload capacity
3.1 Choice of specific electric loading
A large value of ac results in higher copper losses &
higher
temperature rise. For machines with high voltage rating smaller
values of ac
should be prepared. Since for high voltage machines the space
required for
insulation is large.
For high overload capacity, lower values of ac should be
selected.
Since large values of ac results in large number of turns per
phase, leakage
reactance will be high. Large values of leakage reactances
results in reduced
overload capacity.
3.2 Choice of specific magnetic loading
With large values of Bav, the magnetizing current will be high,
which
results in poor power factor. However in induction motors the
flux density in
the airgap should be such that there is no saturation in any
part of the magnetic
circuit.
A large value of Bav results in increased iron loss &
decresed
efficiency. With higher values of Bav higher values of over load
capacity can
be obtained. Since the higher Bav provides large values of flux
per pole, the
turns per phase, will be less & so the leakage reactance
will be less. Lower
value of leakage reactance results in higher over load
capacity.
4. Main Dimensions
The main dimensions of induction motor are the diameter of
stator
bore,D & the length of stator core,L.
In induction motors most of the operating characteristics are
decided
by L/ ratio of the motor.
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L/ ratio
For minimum cost 1.5 to 2
For good power factor 1 to 1.25
For good efficiency 1.5
For good overall design 1
5.Stator winding
For small motors upto 5HP, single layer windings like mush
Winding, whole coil concentric winding & bifurcated
concentric
winding are employed.
For large capacity machines, double layer windings(either lap
or
wave winding) are employed with diamond shaped coils.
5.1 Stator turns per phase
The turns per phase Ts, can be estimated from stator phase
voltage and maximum flux in the core. The maximum flux(m) in
the
core can be estimated from Bav,D,L and p.
Bav = pm/DL
Stator turns per phase = Es/(4.44*Kws*f*m)
Es = Stator phase voltage
5.2 Length of mean turn
The Length of mean turn for voltage upto 650 Vcan be
calculated by
Length of mean turn = 2L+2.3 +0.24
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5.3 Stator conductors
The area of cross section (as) of stator conductors can be
estimated from the knowledge of current density, KVA rating of
the
machine & stator phase voltage.
Stator phase current,Is = Q/(3Es*10-3)
as=Is/s
as=ds2/4
6. Stator Core
The design of stator core involves selection of number of
slots,
estimation of dimensions of teeth and depth of stator core.
6.1 Stator slots
Different types of slots are
1. open slots
2. semi enclosed slots
When open slots are used the winding coils can be
formed and fully insulated before installing & it is easier
to
replace the individual coils. Another advantage is that we
can
avoid excessive slot leakage thereby reducing the leakage
reactance.
When semienclosed slots are used the coils must be
taped & insulated after they are placed in the slots.
The
advantages of semienclosed slots are less airgap contraction
factor giving a small value of magnetising current, low
tooth
pulsation loss & much quieter operation.
In small motors round conductors are used and in large
& medium size mototrs strip conductors are used.
6.2 Choice of stator slot
Number stator slots depends on
1. tooth pulsation loss
2. leakage reactance
3. ventilation
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4. magnetizing current
5. iron loss
6. cost
stator slot pitch,yss = Gap surface/Total no. of stator
slots
Total no. of stator slots = Ss
Gap surface = D
Total no. of stator slots = No. of phases*Conductors per
phase
= 3*2Ts
Conductors per slot,Zss = Total no. of stator slots/Ss
6.3 Area of stator slot
Area of each slot = Copper area per slot/space factor
= Zss*as/ space factor
After obtaining the area of the slot, the dimensions of the
slot
should be adjusted. The slot should not be too wide to give
a
thin tooth.
6.4 Stator teeth
Minimum teeth area per pole = m/1.7
Teeth area per pole = (Ss/p)*Li*Wts
Minimum width of teeth, Wts= m/(1.7*Ss/p*Li)
The minimum width of stator tooth is either near the
gap surface or at one third height of tooth from slot
opening.
6.5 Depth of stator core
The Depth of stator core depends on the flux density in the
core.
Depth of stator core = m/(2*Bcs*Li)
Bcs = Flux desity in stator core
7.Length of air gap
Length of air gap is decided by
1. Power Factor
2. Pulsation loss
3. cooling
4. Over load capacity
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5. Unbalanced magnetic pull
6. Noise
8. Choice of rotor slots
With certain combination of stator and rotor slots, the
following
problems may develop in the induction motor.
1. The motor may refuse to start
2. The motor may crawl at some subsynchronous speed
3. Severe vibrations are developed & so the noise will be
excessive
The above effects are due to harmonic magnetic fields
developed in the machine. The harmonic fields are due to
1. winding
2. slotting
3. saturation
4. irregularities in air gap
The harmonic fields are superposed upon the fundamental sine
wave field & induce emfs in the rotor windings & thus
circulate
harmonic currents. These harmonic currents in turn interact with
the
harmonic fields to produce harmonic torques.
Harmonic induction torque
Harmonic induction torques are torques produced by harmonic
fields
due to stator winding and slots.
Harmonic synchronous torque
Harmonic synchronous torques are torques produced by the
combined
effect of same order of stator & rotor harmonic fields.
Crawling
Crawling is a phenomena in which the induction motor runs at a
speed
lesser than subsynchronous speed.
Cogging
Cogging is a phenomena in which the induction motor refuse to
start.
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Synchronous Cusps
Synchronous Cusps are the synchronous torques produced due
to
harmonic synchronous speeds. Due to Synchronous Cusps the
machine
will crawl.
Vibration & Noise
The teeth being cantilevers respond to varying forces and set
into
vibrations. Thus noise is produced.
9. Design of squirrel cage rotor
It consists of
1. laminated core
2. Rotor bars
3. End rings
Diameter of rotor,Dr = D-2lg;
lg-length of air gap
Design of rotor bars & slots
Rotor bar current is given by
Ib = (6*Is*Ts*Kws*Cos)/Sr
Area of each rotor bar is given by
ab = Ib/b in mm2
Advantages of closed slots
1. Low reluctance
2. less magnetising current
3. Queiter operation
4. Large leakage reactance & so starting current is
limited
Disadvantages of closed slots
Reduced over load capacity
Design of end rings
It can be shown that if flux distribution is sinusoidal then the
bar
current & end ring current will also be sinusoidal.
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Maximum value of end ring current,Ie(max) = (Sr*Ib(max))/2*p
However current is not maximum in all the bars under one pole at
the
same time but varies according to sine law, hence the maximum
value
of the current in the endring is the average value of the
current of half
the bars under one pole.
Maximum value of end ring current,Ie(max) = (Sr*Ib(ave))/2*p
RMS value of end ring current,Ie = Ie(max)/1.414
Area of cross section of end ring ae= Ie/e in mm2
Also
Area of cross section of end ring ae = de*te;
de - depth of end ring;
te - Thickness of endring
10. Design of wound rotor
The wound rotor has the facility of adding external resistance
to rotor
circuit in order to improve the torque developed by the motor.
The
rotor consists of laminated core with semi-enclosed slots and
carries a
3 phase winding.
10.1 Rotor windings
For small motors mush windings are employed.
For large motors double layer bar type wave windings are
employed.
10.2 Number of rotor turns
Number of rotor turns can be calculated by
Number of rotor turns,Tr = (Kws*Ts*Er)/(Kwr*Es)
Ts - Number of stator turns
Rotor current , Ir = (0.85*Is*Ts)/Tr
Area of rotor conductor,ar = Ir/r
10.3 Number of rotor slots
With certain combination of stator and rotor slots, the
following
problems may develop in the induction motor.
1. The motor may refuse to start
2. The motor may crawl at some subsynchronous speed
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3. Severe vibrations are developed & so the noise will
be
excessive
The above effects are due to harmonic magnetic fields
developed in the machine. The harmonic fields are due to
1. winding
2. slotting
3. saturation
4. irregularities in air gap
10.4 Rotor teeth
Minimum teeth area per pole = m/1.7
Teeth area per pole = (Sr/p)*Li*Wtr
Minimum width of teeth, Wtr= m/(1.7*Sr/p*Li)
Minimum width of teeth, Wtr=[(Dr-2dsr)/Sr]-Wsr
10.5 Rotor core
Depth of rotor core dcr = m/(2*Bcr*Li)
Where
Bcr= Flux density in the rotor core
Inner diameter of rotor lamination, Di = Dr-2(dsr+dcr)
Where dcr = depth of rotor core
10.6 Slip rings & brushes
The wound rotor consists of 3 slip rings mounted on the
shaft
but insulated from it. The rings are made of either brass or
phosphor bronze.
The brushes are made up of metal graphite. The brush
dimensions are decided by assuming a current density of 0.1
to
0.2 A/mm2
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UNIT V
Synchronous Machine
Consists of
- Introduction
- Output equation
- Choice of specific magnetic loadings
- Choice of specific electric loadings
- Short Circuit Ratio
- Length of airgap
- Number of stator slots
- Field design
- Computer Aided Design of Electrical Machines
1. Introduction
The synchronous machines may be classified into
(i) Salient pole machines
(ii) Cylindrical rotor machines
(i) Salient pole machines
These are driven by water wheels or diesel engines. They operate
at
low speeds and so large number of poles is required to produce
desired
frequency. This type of machine has projecting poles and field
coils are
mounted on the poles.
(ii) Cylindrical rotor machines
These are driven by steam turbines and gas turbines which run at
very
high speeds. They have slots on the periphery of smooth
cylindrical
rotor. The field conductors are placed on these slots.
2. Output Equation
Output equation of ac machine is relation of KVA rating of
the
machine to the specific loadings and main dimensions.
KVA ,Q = Co*D2*L*ns
Output coefficient,Co = 11Kws*Bav*ac*10-3
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3. Choice of Specific magnetic loading
The choice of Bav depend on
(i) Iron loss
(ii) Stability
(iii) Voltage rating
(iv) Parallel operation
(v) Transient short circuit current
i) High Bave which results in high flux density in the teeth and
core which results in
high iron loss gives higher temperature rise.
ii) high Bave which results in low Tph which results in low
leakage reactance (Xl )
gives high short circuit current
iii) In high voltage machines slot width required is more to
accommodate
thicker insulation which results in smaller tooth width which
results in small
allowable Bave
iv) stability : Pmax =V*E/Xs . Since high Bave gives low Tph and
hence low Xl
Pmax increases and improves stability.
v) Parallel operation : Ps = (VE sin)/Xs ; where is the torque
angle. So
low Xs gives higher value for the synchronizing power leading
stable parallel
operation of synchronous generators.
Guide lines : Non-salient pole alternator : 0.54 0.65 Wb/m2
Salient pole alternator : 0.52 0.65 Wb/m2
4. Choice of specific Electric loading (ac)
It depends on the following
(i) Copper loss
(ii) temperature rise
(iii) Operating voltage
(iv) Synchronous reactance
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(v) Stray load losses
i) Copper loss and temperature rise: High value of ac Copper
loss and temperature
rise higher copper loss leading high temperature rise. So choice
of depends on the
cooling method used.
ii) Operating voltage : High voltage machines require large
insulation and so the
slot space available for conductors is reduced. So a lower value
for ac has to be
chosen.
iii) Synchronous reactance (Xs) : High value of ac results in
high value of
Xs , and this leads to a) poor voltage regulation b) low steady
state stability limit.
iv) Stray load losses increase with increase in ac.
Guide lines : Non-salient pole alternators : 50, 000 75,000
A/m
Salient pole alternators : 20,000 40,000 A/m
5. Short Circuit Ratio (SCR)
SCR = Field current required to produce rated voltage on
opencircuit
Field current required to produce rated current on short
circuit
= 1/ direct axis synchronous reactance = 1/Xd
Thus SCR is the reciprocal of Xd , if Xd is defined in p.u.value
for rated voltage
and rated current. But Xd for a given load is affected by
saturation conditions that
then exists, while SCR is specific and univalued for a given
machine.
Non-salient pole alternators : 1- 1.5 ; Salient pole alternators
: 0.5 0.7
Effect of SCR on machine performance
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i) Voltage regulation : A low SCR high Xd which results in large
voltage drop
which results in poor voltage regulation..
ii) Parallel operation : A low SCR which results in high Xd
which results in low
synchronizing power which results in parallel operation
becomes difficult.
iii) Short circuit current : A low SCR which results in high Xd
which results in
low short circuit current. But short circuit current can be
limited by other means not necessarily by keeping a low
value of SCR.
iv) self excitation : Alternators feeding long transmission
lines should
not be designed with small SCR as this would lead to large
terminal voltage on open circuit due to large capacitance
currents.
Summarizing ,high value of SCR leads to
i) high stability limit
ii) low voltage regulation
iii) high short circuit current
iv) large air gap
The present trend is to design machines with low value of SCR,
this is due to the
recent development in fast acting control and excitation
systems.
6. Length of airgap
The length of air gap very much influences the performance of a
synchronous
machine. A large airgap offers a large reluctance to the path of
the flux produced
by the armature MMF and thus reduces the effct of armature
reaction. Thus a
machine with large airgap has a small Xd and so has
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i)small regulation
ii) high stability limit
iii) high synchronizing power which makes the machine less
sensitive to load variations
iv) better cooling at the gap surface
v) low magnetic noise and smaller unbalanced
magnetic pull.
But as the airgap length increases, a large value of Field MMF
is required
resulting in increased cost of the machine.
7. Number of stator slots
Factors to be considered in the selection of number of slots
:
1. Balanced 3-phase winding to be obtained
2. With large number of slots
i) which results in large number of coils gives increased labour
cost
ii) cooling is improved
iii) tooth ripples are less
iv) Flux density in the iron increases due to decreased tooth
width.
Guide lines : Slot pitch (ys ) 25 mm for low voltage
machines;
40 mm for machines upto 6 kV ;
60 mm for machines upto 15 kV.
7.1. Methods of Eliminating Harmonics
By using
i) distributed windings
ii) fractional coil pitch
iii) fractional slot windings
iv) skewing
v) large airgap
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Further calculations needed after determining D and L :
i) Flux per pole = = Bave ( DL/p )
ii) Tph is calculated from the EMF equation taking Eph = Vph
iii) Iph = (Qx 103 ) / 3 VL
iv) Armature MMF/pole = Ata = 2.7 Iph Tph Kw /p
v) Effective area per pole = 0.6 0.65 times actual area
8. Field Design (Salient poles)
Data needed for the design of the Field winding:
i) Flux density in the pole core
ii) Winding depth (df)
iii) Leakage factor (pole flux/gap flux)
iv) Field winding space factor (Sf)
v) Power dissipation (qf) in W/m2
vi) The ratio of field MMF to armature MMF
vii) Allow about 30 mm for insulation , flanges and height of
the pole
shoe.
MMF per unit height of the winding = 104 Sqrt (Sf df qf )
9. Computer Aided Design of Electrical Machines
The process of design any electrical may be broadly divided into
three major
aspects:
i) Electrical design
ii) Mechanical design
iii) Thermal design. Even though, these problems can be
solved
separately, there are many inter- related features.
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The advantages of computer aided design are :
i) The computer can handle large volume of data to make a
number of trial designs.
ii) Speed and accuracy of calculations are very high.
iii) It can be programmed to satisfying take logical
decisions
iv) An optimized design with least cost and the required
performance can be easily obtained.
Generally any design method can be
i) Analysis method
ii) Synthesis method
iii) Hybrid method
In the analysis method of design , a preliminary design is made
by the designer
regarding the machine dimensions, materials and other
constructional features and
these are given as input data to the computer and the
performance quantities are
calculated. The designer examines the performance and
accordingly alters the input
data and then feed them to the computer again. The computer
calculates the new
performance with the revised data. This process is repeated till
the required
performance is achieved.
In the synthesis method, the required performance values are
also given to the
computer as input. The computer through an iterative process
alters the dimensions
till the required performance is obtained.
In the hybrid method, by some human intervention, a combination
of analysis and
synthesis methods are adopted.
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The method of design optimization using computers :
i) Choice of independent variables
ii) Variable transformation
iii) Forming the constraint functions for the performance
iv) Forming the objective function (OBJ)
v) Applying the minimization technique till the OBJ becomes with
in the
chosen tolerance.
Example of Design of optimization of Induction Motors
The independent variables which has a significant effect on the
performance are
stator core diameter, stator core length , stator core depth,
stator slot depth, stator
slot width, rotor slot depth, rotor slot width, end ring depth,
end ring width, .
airgap length and airgap flux density.
The other variables in the design are either taken as constants
dased on the voltage
and power rating of the machine or they are in some way related
to the above 11
variables.
During the course of optimization when the variables undergo
incrementing or
decrementing, they should also be constrained to be with in
practical ranges. This is
obtained by variable transformation. For example for airgap Xact
= X tran + Lg min
; where they respectively denote actual and transformed values
and Lg min =
minimum airgap required.
Performance Specifications:
1. Starting torque
2. maximum torque
3. Full- load power factor
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4. full -load efficiency
5. full load slip
6. tooth and core flux densities
7. starting current
8. temperature rise
9. cost of the machine.
Objective function
The objective function is formed by comparing the specified and
calculated values
of the performance quantities at each iteration. Objective
function minimization
can be carried out either using conventional methods such as
Powels algorithm or
Rosenbrock method or the recent techniques such as Genetic
algorithm.
It should be noted that the independent variables or the
performance specifications
vary with the type of machine and its application.